
The Guyou hemisphere-in-a-square projection is a
conformal
Conformal may refer to:
* Conformal (software), in ASIC Software
* Conformal coating in electronics
* Conformal cooling channel, in injection or blow moulding
* Conformal field theory in physics, such as:
** Boundary conformal field theory ...
map projection
In cartography, map projection is the term used to describe a broad set of transformations employed to represent the two-dimensional curved surface of a globe on a plane. In a map projection, coordinates, often expressed as latitude and longit ...
for the hemisphere. It is an oblique aspect of the
Peirce quincuncial projection.
History
The projection was developed by of France in 1887.
Formal description
The projection can be computed as an oblique aspect of the Peirce quincuncial projection by rotating the axis 45 degrees. It can also be computed by rotating the coordinates −45 degrees before computing the stereographic projection; this projection is then remapped into a square whose coordinates are then rotated 45 degrees.
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The projection is conformal except for the four corners of each hemisphere’s square. Like other conformal polygonal projections, the Guyou is a
Schwarz–Christoffel mapping.
Properties
Its properties are very similar to those of the
Peirce quincuncial:
* Each hemisphere is represented as a square, the sphere as a rectangle of aspect ratio 2:1.
* The part where the exaggeration of scale amounts to double that at the centre of each square is only 9% of the area of the sphere, against 13% for the Mercator and 50% for the stereographic
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* The curvature of lines representing great circles is, in every case, very slight, over the greater part of their length.
* It is conformal everywhere except at the corners of the square that corresponds to each hemisphere, where two meridians change direction abruptly twice each; the Equator is represented by a horizontal line.
* It can be
tessellated in all directions.
Related projections
* The
Adams hemisphere-in-a-square projection
The Adams hemisphere-in-a-square is a conformal map projection for a hemisphere. It is a transverse version of the Peirce quincuncial projection, and is named after American cartographer Oscar Sherman Adams, who published it in 1925.. When it i ...
and the
Peirce quincuncial projection are different aspects of the same underlying Schwarz–Christoffel mapping. Such mappings are transformations of half a
stereographic projection
In mathematics, a stereographic projection is a perspective projection of the sphere, through a specific point on the sphere (the ''pole'' or ''center of projection''), onto a plane (the ''projection plane'') perpendicular to the diameter th ...
.
See also
*
List of map projections
This is a summary of map projections that have articles of their own on Wikipedia or that are otherwise notable
Notability is the property
of being worthy of notice, having fame, or being considered to be of a high degree of interest, signif ...
References
{{Map projections
Map projections
Conformal projections